FPGA designs of parallel high performance GF(2233) multipliers [cryptographic applications]

For many applications from the areas of cryptography and coding, finite field multiplication is the most resource and time consuming operation. We have designed and optimized four high performance parallel GF(2²³³) multipliers, for an FPGA realization, and analyzed the time and area complexities. One of the multipliers uses a new hybrid structure to implement the Karatsuba algorithm. For increasing performance, we make excessive use of pipelining and efficient control techniques and use a modem state-of-the-art FPGA technology. As a result we have, to our knowledge, the first hardware realization of subquadratic arithmetic and currently the fastest and most efficient implementation of 233 bit finite field multipliers.